The offer, believed to be between £10-11million, has been submitted as the Gunners test the resolve of the Catalan giants to hang on to Spain's all-time record goalscorer.

Wenger has admitted his interest in Villa but said this week that Barcelona have resisted selling the 31-year-old and his public stance is that the move is “dead”.

However, privately Arsenal have been given encouragement that a deal could still be possible on the last day of the window and are preparing to make one final push for the forward.

Spanish sources have told Goal.com that Villa is “very keen” to join Arsenal after growing frustrated with his lack of opportunities at Camp Nou.

He was an unused substitute for Barcelona in the 1-1 Copa Del Rey semi-final first leg against Real Madrid at the Bernabeu on Wednesday night.

Goal.com revealed on Monday that the club’s transfer and contract negotiator Dick Law had been in Spain to negotiate the transfer of the country’s all-time leading goalscorer.

The Londoners were knocked back by Barcelona when they made an approach for Villa earlier this month.

But Wenger has refused to accept defeat in his pursuit of the forward and is prepared to pay up to £13.8m to sign him on a permanent deal and match his current £110,000-a-week wages.

Negotiations have centred on the construction of the deal, with Barcelona still owing Arsenal scheduled payments for the transfers that took Cesc Fabregas and Alex Song to Camp Nou in the summers of 2010 and 2011.

Wenger wants a marquee signing to galvanise both the supporters and the playing squad as the club attempt to secure a top-four league finish and negotiate a round-of-16 Champions League tie against last season’s runners-up Bayern Munich.

Although Villa played the whole 90 minutes in Barcelona’s 5-1 win over Osasuna last Sunday – his first full match since November 2011 – he has started just 12 of the club’s 36 matches this season, including only seven out of a possible 21 in La Liga.

Arsenal had made bolstering their strikeforce a top priority in the window and bid around £10m for Atletico Madrid’s Adrian Lopez a month ago but they are now concentrating all their efforts on Villa.

Barcelona had been reluctant to off-load such a valuable asset ahead of a twin assault on the Champions League and La Liga titles, and the club’s public stance has been that the striker will stay at least until the summer. “David is not going to leave,” coach Tito Vilanova said a fortnight ago. “We are very happy with him.”

Privately, the Spanish club accept that they might have to grant his wish of a switch this month and cash in on a player who only has 18 months remaining on his contract.

Villa, who missed much of last season after breaking his leg, is Barca’s second-leading scorer in 2012/13 with 10 goals, behind only Lionel Messi, who has netted an astonishing 44 times.